设计空间几何过滤与流形重构增强的层流翼梯度优化设计方法

doi:10.7527/S1000-6893.2025.31917

Abstract

Abstract:

The discrete adjoint-based gradient optimization method is one of the pivotal technical approaches for achieving laminar drag reduction optimization. However， the sensitivity of laminar wing transition location and aerodynamic performance of laminar wings to variations in pressure distribution makes the aerodynamic optimization problem under multiple constraints highly nonlinear and prone to prominent multimodality. These challenges significantly increase the optimization difficulty of gradient-based methods and compromise their robustness. This paper introduces a design space reconstruction method based on geometric smoothing and the geometric representation of Grassmann manifolds， which filters out high geometrical distorted configurations and maps the high-dimensional design space to a more compact low-dimensional design space without geometric constraints. Coupled with the discrete adjoint method， a design space geometric filtering and manifold reconstruction-enhanced gradient optimization design method for laminar flow wings has been developed. Aerodynamic optimization studies on the RAE2822 airfoil using different geometric parameterization forms demonstrate that the proposed method significantly reduces the dependence of optimization results on specific parameterization schemes， and greatly improves algorithmic robustness compared to traditional gradient-based approaches. The gradient optimization method proposed in this paper is of significant importance for the development of efficient aerodynamic optimization technologies for full-aircraft laminar wings in practical engineering applications.

Key words: discrete adjoint, gradient optimization, Grassmann manifold, geometric smoothing, laminar flow drag reduction

CLC Number:

V221.3

Jiecheng DU, Hanyue RAO, Tihao YANG, Junqiang AI, Yifu CHEN, Yayun SHI, Junqiang BAI. Design space geometric filtering and manifold reconstruction-enhanced gradient optimization design method for laminar flow wing[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(20): 531917.

Figures/Tables 22

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Table 1

Gradient verification of lift coefficients CL with respect to geometric design variables

设计变量	有限差分梯度求解	伴随方法梯度求解	相对误差	有限差分最优步长
1	1.276 958 65	1.276 399 84	4.4×10^-4	$10 - 4$
2	0.051 376 05	0.051 312 79	1.2×10^-3	$10 - 2$
3	-1.684 265 89	-1.680 759 95	2.1×10^-3	$10 - 3$
4	0.216 327 58	0.216 836 85	2.4×10^-3	$10 - 3$
5	-1.182 558 32	-1.182 324 15	2.0×10^-4	$10 - 3$
6	-2.292 609 26	-2.296 505 80	1.7×10^-3	$10 - 2$
7	-0.138 632 92	-0.138 272 93	2.6×10^-3	$10 - 3$
8	4.871 485 11	4.872 950 09	3.0×10^-4	$10 - 2$
9	-1.749 228 06	-1.747 886 82	7.7×10^-4	$10 - 5$
10	0.203 673 58	0.203 098 64	2.8×10^-3	$10 - 4$

Table 1

Table 2

Gradient verification of drag coefficients CD with respect to geometric design variables

设计变量	有限差分梯度求解	伴随方法梯度求解	相对误差	有限差分最优步长
1	0.003 166 59	0.003 169 59	9.5×10^-4	$10 - 5$
2	-0.004 478 11	-0.004 471 91	1.4×10^-3	$10 - 7$
3	0.001 094 61	0.001 085 04	8.7×10^-3	$10 - 4$
4	-0.007 263 53	-0.007 268 56	6.9×10^-4	$10 - 4$
5	0.002 299 12	0.002 298 48	2.8×10^-4	$10 - 4$
6	-0.002 595 68	-0.002 593 99	6.5×10^-4	$10 - 3$
7	-0.003 835 43	-0.003 831 68	9.8×10^-4	$10 - 3$
8	0.020 255 05	0.020 269 08	6.9×10^-4	$10 - 2$
9	0.003 883 85	0.003 888 47	1.2×10^-3	$10 - 6$
10	-0.001 175 41	-0.001 176 31	7.7×10^-4	$10 - 3$

Table 2

Fig.6

Table 3

Fig.7

Fig.8

Table 4

Turbulent optimized results comparison

构型	$C L$	$C D$	$Δ C D$	AoA/（°）
RAE 2822	0.77	0.015 29		2.30
GOM	0.77	0.011 43	0.003 87	1.75
MLE-GOM	0.77	0.011 58	0.003 71	1.11

Table 4

Fig.9

Fig.10

Fig.11

Fig.12

Table 5

Table 6

Natural laminar optimized results comparison

构型	$C L$	$C D$	$Δ C D$	AoA/（°）	x_{t_u}/c	x_{t_l}/c
RAE2822	0.78	0.010 67		2.00	0.372	0.459
GOM-F1	0.78	0.006 48	0.004 19	1.73	0.531	0.454
MLE-GOM-F1	0.78	0.006 81	0.003 86	1.74	0.478	0.476
GOM-F2	0.78	0.006 16	0.004 51	1.65	0.564	0.491
MLE-GOM-F2	0.78	0.005 03	0.005 64	1.90	0.747	0.596

Table 6

Fig.13

Fig.14

Fig.15

Fig.16

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条目	参数	数量	下限	上限
目标	C_D	1
约束	C_L	1
	V/m³	1	0.95V₀	1.02V₀
	t/m	10	0.9t₀

条目	参数	数量	下限	上限
目标	C_D	1
约束	C_L	1
	V/m³	1	0.95V₀	1.02V₀
	t/m	10	0.9t₀

Design space geometric filtering and manifold reconstruction-enhanced gradient optimization design method for laminar flow wing

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